Preface

``... since every piece of matter in the Universe is in some way affected by every other piece of matter in the Universe, it is in theory possible to extrapolate the whole of creation ­ every sun, every planet, their orbits, their composition and their economic and social history from, say, one small piece of fairy cake.''

Douglas Adams, ``The Restaurant at the End of the Universe'',
Ballantine Books, New York 1995

This is a book about correlations in quantum many­body systems in equilib­ rium and nonequilibrium and the powerful approach of nonequilibrium Green's functions and quantum kinetic equations. It contains some 40 articles written by leading experts which are devoted to fundamental questions of the theory and to modern applications in a variety of fields including condensed matter, plasmas and nuclear matter. The scope of phenomena considered is very broad covering Bose condensation and QCD, quantum transport and femtosecond spectroscopy, plasma oscillations and plasma turbulence, heavy ion beam collisions and particle production, coherent control and intense laser­matter interaction, bound states, impact ionization, tunneling and much more.

A theory which is capable to describe, from first principles, such a diversity of phenomena must be unusual. Its foundations were laid in the 1950ies by Julian Schwinger, Paul Martin and their students, and it was brought to perfection by Gordon Baym and Leo Kadanoff when they formulated their famous equations fourty years ago. These remarkable early days come back to life in the amazing very personal articles of Paul and Gordon who also give credit to the many brilliant scientists involved in these developments.
The fascination and success of nonequilibrium Green's functions theory arises from its internal consistency, conserving character and powerful diagrammatic tools. Its field­theoretical foundation has made applications to new types of particles and interactions, other physical systems or energy ranges a straightforward exercise. While originally intended to describe many­particle systems close to equilibrium, the last 20 years have witnessed the successful application of the Kadanoff­Baym equations to situations far from equilibrium, such as nuclear collisions and laser or high­field excitation of condensed matter. Besides, recent progress in computer power has made direct numerical solutions of quantum kinetic equations, including the two­time Kadanoff­Baym equations possible.

These recent advances led me to the (crazy) idea to invite theorists who use nonequilibrium Green's functions in various fields to an interdisciplinary workshop to exchange their experience. Besides, invitations were sent to founders of the theory (with, admittedly, very limited optimism). So the overwhelming response was a true surprise and eventually culminated in the interdisciplinary workshop ``Kadanoff­Baym equations. Progress and Perspectives for Many­ Body Physics'', which took place in Rostock, Germany, September 20­24 1999. The unusual setting that everybody, most of the time, was not an expert and, when he was, he had to make himself clear to mostly non­experts, turned out to be very fruitful for a deeper understanding of many fundamental questions. This has had valuable influence on this book too.

So, what have we learned at this meeting? Despite deep differences in subjects, approximations and notation, it is my impression that there emerged a number of questions which appear to be of similar importance for the future of most fields: First, the development of consistent approximation schemes (e.g. \Phi-derivable approximations). Second, new applications to situations far from equilibrium (which involves further analysis of the Generalized Kadanoff-Baym ansatz or gradient expansions). Third, active development of direct numerical solutions of quantum kinetic equations. Fourth, the necessity to develop alternative approaches too which may successfully complement nonequilibrium Green's functions (this includes quantum Monte Carlo and quantum molecular dynamics). Finally, as it is convincingly formulated in Paul Martin's paper, there still remain open fundamental questions which are worth investigation (for which simple models are best candidates).

The present book is based on talks and posters at this workshop. In accord with its interdisciplinary character, each field is introduced by one or several review articles, shorter papers were combined into larger ones. Articles were refereed by workshop participants not only with respect to scientific correctness but also with respect to general understandability and proper reference to activities in other fields. To further improve the use of this book, each chapter is preceded by a brief introduction which, among others, establishes relations to other parts and includes cross references to further papers. The book is concluded by a detailed subject index and, as a special service to readers, an index of names (which includes references to cited papers and to names mentioned in the text). Thus, I hope the present book will be of interest and value to graduate students and to scientists working in a large variety of fields who are interested in nonequilibrium Green's functions.

A lot of effort was necessary to get this book done. First of all, of course, it required excellent manuscripts but also the willingness of authors to adjust to a broad, non­specialized readership. Secondly, the book benefited from ac­ tive participation of many contributors (in particular, I am grateful to Gordon Baym, Pawel Danielewicz, Hartmut Haug, Antti­Pekka Jauho, Jörn Knoll, Sigurd Köhler and Dietrich Kremp) in the preparation of the workshop and of this book ­ by suggesting topics and workshop participants and in carefully refer­ eeing manuscripts. Third, a lot of technical problems, including reformatting and editing of manuscripts, could be solved only due to the remarkable work of Renate Nareyka and Dirk Semkat. Many thanks also to Thomas Bornath and Wolf Kraeft for proof reading. Finally, it is my pleasure to acknowledge the generous financial support from the Deutsche Forschungsgemeinschaft and Rostock University without which this workshop and thus, the present book, would not have been possible.

Michael Bonitz, Rostock, January 2000